lefteris_kaliamboswikiaorg-20200214-history
CORRECT HISTORY OF MATH
By Prof. Lefteris Kaliambos (Natural Philosopher in New Energy) November 7, 2018 After my paper "CORRECT HISTORY OF PHYSICS" based on my discovery of the dipole nature of photonpresented in 1993 at the intenational conference "Frontiers of funsamental physics" (Kaliambos Natural philosophy) and also the nuclear force and structure (2003), it was necessary to modify the history of math, because I discovered that both the Parthenon (438 BC) and the Hephaestion tomb(320 BC) contain the math of the golden section availαble from the time of the building of the Great Pyramid (2560 BC). Today choosing in Google the topic “HISTORY OF MATHEMATICS” we see that the most useful is the article “History of mathematics-Wikipedia”. Under a large number of scientific advances Wikipedia starts with the most ancient mathematical texts available from Mesopotamia and Egypt - Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000–1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples of the well-known Pythagorean theorem of Greek mathematics. (570 - 490 BC). However after my discoveries of the mathematics of the Great pyramid, the Parthenon math, the math of Caryatides, the math of Alexandrian walls, and the mathematical tomb of Hephaestion, today it is well-known that the Egyptian mathematicians of the Great pyramid (2560 BC) and also Pheidias and Denocrates used not only the math of the Pythagorean theorem but also the mathematics of the golden section. In this case the golden number Φ = 1.618034 was taken from the first letter of Pheidias (Φειδίας). Here I present the photo of Parthenon, because it contains the math of the golden section and of the Pythagorean theorem from the primordial time of the building of the great pyramid. After my discoveries of the golden section today it is well-known that Babylonians found the math of the golden section by drawing a pentagonal scheme of side α = 1 (unit of length). Then, surprisingly they observed that the diagonal δ in units of length is equal to Φ = 1.618034 given by the relation 1 + Φ = Φ2 or Φ2 - Φ - 1 = 0. Thus today applying this quadratic equation and solving for Φ in units of length one gets Φ = (1 + 50.5)/2 = 1.618034 In my researches for revealing the math of the Great Pyramid I have found that the Egyptian mathematicians used a theoretical sacred cone with a circular base of r = 1 (unit of length = 115.17 m) since r = α/2 = 230.34 m / 2.(Great pyramid of Giza -Wikipedia). The cone included also the height h = Φ0.5 = 1.272 with the slant height L ( hypotenuse) = Φ = 1.618034. Under this condition applying the Pythagorean theorem we get (1)2 + (1.272)2 = (1.618034)2 = 2.618034 or 1+ (Φ0.5)2 = Φ2 or 1 + Φ = Φ2 Therefore, in order to know from Wikipedia a detailed history of math before the birth of Pythagoras (570 BC) we see that the history of the math of the golden section is absent. Here I clear that after my detailed research about the math of the Great Pyramid of Giza I published my paper “ Parthenon math and great pyramid” because I found the mathematical relation of Parthenon with the pyramid. In the article “Great Pyramid -Wikipedia” is described the perfect square of the base of the pyramid having a side α = 230.34 m. That is, r = 230.34/2 = 115.17 m , because the square of the pyramid includes the circle C = 2πr of the theoretical sacred cone. In Wikipedia is also described the initial height h = 146.5 m. That is, h = rΦ0.5 = 146.5 m. In other words in the absence of a detailed knowledge about the Egyptian mathematics of the golden section in Wikipedia the height h = 146.5 m is not related with the math of the golden section. Such a pyramid was believed to be a sacred pyramid because I have found that it includes a theoretical sacred cone with the relation of mystic numbers π and Φ0.5 given by π = 4/Φ0.5 = 4/1.272 = 3.1446 which is close to π = 3.14159… Another ratio does appear throughout most of the Parthenon. This equals a 9 : 4 ratio which can be related to the sacred Pythagorean rectangles of the numbers 3, 4, and 5. According to the history of Greek People (Volume Γ2 page 282) the dimensions of the Parthenon are Height z = 13.724 m . Width y = 30.88 m. Length x = 69.48 m Now for calculating the height (H = 1811.3 m) of the theoretical pyramid existing over the temple along a vertical direction toward to the sky I was based on the "GREEK SURNAMES: Τα μαθηματικά του Παρθενώνα” The columns in Parthenon actually lean slightly inwards so that if they carried on they would make a very tall theoretical pyramid with a volume Vt = Vc /2 where Vt is the volume of the theoretical pyramid of Parthenon and Vc is the volume of the Cheops pyramid. Under this condition we write Vt = xyH/3 = Vc / 2 = α2h/6 or xyH = α2h/2 Here y = 30.88 m is the width of the Parthenon and x = (9/4)y is the length . On the other hand α is the side of the square of the Great Pyramid and h is the height h = αΦ0.5/2. Under this condition we may write y2H = (4/9)(α3Φ0.5/4) or H = (4/9)(Φ0.5/4)( α3/y2) or H = (Φ0.5 α3) / (3y)2 Then we see that the height (H = 1811.3 m) of the theoretical pyramid of Parthenon depends on the dimension y of Parthenon and the side α of the Cheops square pyramid including the Pythagorean number 3 , and the golden number Φ0.5 . That is, the vertical line (H= 1811.3 m) existing over the head of the goddess of the wisdom should contain all knowledge of mathematics from Cheops to Thales and to Pythagoras. Then, since y = 30.88 m and α = 230.34 m we get H = (Φ0.5 α3) / (3y)2 = 1811.3 m Finally I discovered also that in Parthenon there are many geometric constructions of the Golden Ratio based on a golden rectangle whose ratio of the longer side to the shorter side is Φ = (1 + 50.5)/2.( Discovery of golden section in Parthenon). Moeover in Caryatides of Acropolis I discovered that the method of designing the golden section is the same as that of the Caryatides in the mathematical Hephaestion tomb. (ΧΡΥΣΗ ΤΟΜΗ). In the article “History of mathematics –Wikipedia “ we also see that Wikipedia continues correctly with many details about the history of math, which I must not repeat, but under my criticism of Wikipedia I emphasize that the beginning of the mathematics contains not only the numbers of the so- called Pythagorean theorem but also the sacred numbers of golden section which did much for the progress of the triumph of Greek architecture. After the math of Parthenon used by Pheidias, also Plato (427 –347 BC) was important in the history of mathematics. His Platonic Academy, in Athens, became the mathematical center of the world in the 4th century BC, and it was from this school that the leading mathematicians of the day, such as Eudoxus of Cnidus, came. It seems also to have been the ancient Greeks who first recognized the fundamental importance of proof in math. The Elements of Euclid give a comprehensive account of Greek achievements up to the beginning of the third century BC called a Hellenistic period with the great mathematicians and astronomers like Aristarchus, (heliocentric system), Eratosthenes, Archimedes, and others. For example using the parallel lines of Euclid’s geometry Eratosthenes was the first man who calculated the perimeter of our earth. Geometry in the hands of the Greeks developed far beyond other branches of mathematics.'' But Greek geometry was able to embrace certain fundamental discoveries now regarded as belonging more naturally to mathematical analysis. The theory of proportion, which Euclid is said to have derived from Eudoxus, paved the way for the sophisticated definitions of the real number system given in the 19th century. The method of exhaustion applied to the investigation of areas and volumes by Euclid, Archimedes, and others already contained the idea of a limit, later to become fundamental in analysis. Apollonius of Perga made significant advances in the study of conic sections. On the other hand Archimedes widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. He also showed one could use the method of exhaustion to calculate the value of π with as much precision as desired, and obtained the most accurate value of π then known, 3.1408 < π < 3.1429. He also studied the spiral bearing his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious method of exponentiation for expressing very large numbers. Moreover after my researches I have found that a simple algebra with linear equations is observed not only in the math of Parthenon but also in the mathematical tomb of Hephaestion. The Hellenistic mathematicians like Hipparchus of Nicaea (c. 190–120 BC) is considered the founder of trigonometry for compiling the first known trigonometric table, and to him is also due the systematic use of the 360 degree circle. Heron of Alexandria (c. 10–70 AD) is credited with Heron's formula for finding the area of a scalene triangle and with being the first to recognize the possibility of negative numbers possessing square roots. Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometry through Menelaus' theorem. The most complete and influential trigonometric work of antiquity is the ''Almagest of Ptolemy (c. AD 90–168), a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Ptolemy is also credited with Ptolemy's theorem for deriving trigonometric quantities, and the most accurate value of π outside of China until the medieval period, 3.1416. Following a period of stagnation after Ptolemy, the period between 250 and 350 AD is sometimes referred to as the "Silver Age" of Greek mathematics. During this period, Diophantus made significant advances in algebra, particularly indeterminate analysis, which is also known as "Diophantine analysis".The study of Diophantine equations and Diophantine approximations is a significant area of research to this day. Among the last great Greek mathematicians is Pappus of Alexandria (4th century AD). He is known for his hexagon theorem and centroid theorem, as well as the Pappus configuration and Pappus graph. Pappus is considered the last major innovator in Greek mathematics, with subsequent work consisting mostly of commentaries on earlier work. The first woman mathematician recorded by history was Hypatia of Alexandria (AD 350–415). She succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. On the other hand the Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon working on a higher level. For example, the first complete arithmetic solution (including zero and negative solutions) to quadratic equations was described by Brahmagupta. (628 AD). However earlier in Alexandria (415 AD) Hepatia was murdered by a mob of Christians led by a lector named Peter. Alsol in 529 AD the Eastern Roman emperor Justinian closed all the Greek schools of philosophy, including Plato’s Academy. Many Greek scholars left the country and some settled in Persia. For this period of decline of Greek mathematics In the "History of mathematics -Wikipedia" we read: "Because of a political dispute, the Christian community in Alexandria had her stripped publicly and executed. Her death is sometimes taken as the end of the era of the Alexandrian Greek mathematics, although work did continue in Athens for another century with figures such as Proclus, Simplicius and Eutocius. Although Proclus and Simplicius were more philosophers than mathematicians, their commentaries on earlier works are valuable sources on Greek mathematics. The closure of the neo-Platonic Academy of Athens by the emperor Justinian in 529 AD is traditionally held as marking the end of the era of Greek mathematics." After a large period of decline and especially during the Scientific Revolution the 17th century saw an unprecedented increase of mathematical and scientific ideas across Europe. Galileo observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. By his position as Brahe's assistant, Johannes Kepler was first exposed to and seriously interacted with the topic of planetary motion. Kepler's calculations were made simpler by the contemporaneous invention of logarithms by John Napier and Jost Bürgi. Kepler succeeded in formulating mathematical laws of planetary motion.The analytic geometry developed by Descartes (1596–1650) allowed those orbits to be plotted on a graph, in Cartesian coordinates. Building on earlier work by many predecessors, Isaac Newton discovered the laws of physics explaining Kepler's Laws, and brought together the concepts now known as calculus. On the other hand it was not until the time of Francois Viete (1590) that the adoption of suitable algebraic notations truly established algebra as a separate study from arithmetic. The work of Viete smoothed the way for the outburst of mathematical invention which took place in western Europe in the 17th century. It made possible the synthesis of algebra and geometry achieved by Rene Descartes (1637). It was Descartes who first attempted to provide a general philosophical frame work for the solution of problems in physics by introducing the fallacious concept of Aristotelian ether which was overthrown not only by Newton’s laws but also by all experiments of modern physics. Nevertheless such philosophical ideas were accepted later by Maxwell and Einstein for developing wrong theories of fields and of relativity which did much to retard the progress of physics. (CORRECT HISTORY OF PHYSICS). What remained aside from a general attitude toward the physical world, was the beginnings of a powerful mathematical technique for representing geometric forms and physical processes in symbolic language which greatly facilitated logical deductions. The new geometry of the well-known Cartesian system with the three dimensions x, y, and z in its turn inspired Isaac Newton and Gottfried Leibniz in their discovery of the calculus. However in spite of its immediate success, the calculus, as it existed in the 18th century, rested on logical inconsistent foundations. This was pointed out by the philosopher George Berkeley (1734), but his criticisms were not met until Augustin Cauchy gave a satisfactory definition of a limit in 1821. The number system, accepted uncritically even by Cauchy, became the object of thorough investigation in the 19th century, and it is to this source that vast revolutions in modern mathematics can be traced. Negative numbers had been manipulated freely but without real understanding.in the 17th century. Hence blind manipulations with the “imaginary” (-1)0.5 were made as early as the 16th century by Jerome Cardan and John Napier (the inventor of logarithms). However, not until Karl Gauss (1831) used number pairs to define the complex numbers were the imaginaries incorporated into a sound analytical theory. The same device clarified the concepts of rational and negative numbers. The problem of the irrationals was attacked by Julius Dedekind, Karl Weierstrass, and Georg Cantor, all of whom gave definitions in terms of infinite classes of rational. The uncritical use of infinite classes later began to produce paradoxes, such as those of Burali-Forti (1897) and Bertrand Russell (1902). This stimulated enormous activity in mathematical logic, which has continued through the 20th century. In the same century after the triumph of the quantum physics (Planck 1900) the experiments of the ionization of hydrogen in the Bohr model (1913) rejected Einstein’s hypothesis of the invalid rest energy of his invalid special relativity (1905) by showing that the energy hν = 13.6 eV of the emitting photon is due not to the mass defect Δm = 13.6 eV/c2 but to the energy Δw = 13.6 eV of the electron-proton interaction in accordance with the conservation law of energy. (EXPERIMENTS REJECT RELATIVITY). Thus the math of the so-called Lorentz trasformations is invalid. Then Schrodinger based on the Bohr model in 1926 in the so-called Quantum Mechanics published his famous equation in three dimensions under the relationship between spherical polar coordinates and Cartesian coordinates x, y, z. Nevertheless Einstein after his invalid general relativity (1915) in which he reintroduced the fallacious ether of the invalid math of the Lorentz transformations in 1938 in his book “The evolution of physics” (page 219) for supporting his strange hypothesis of four dimensions wrote: "Again, the classical physicist splits the four-dimensional continua into the three-dimensional spaces and the one-dimensional time-continuum. The old physicist bothers only about space transformation, as time is absolute for him. He finds the splitting of the four-dimensional world-continua into space and time natural and convenient. But from the point of view of the relativity theory, time as well as space is changed by passing from one c.s. to another, and the Lorentz transformation considers the transformation properties of the four-dimensional time-space continuum of our four-dimensional world of events.” Here I clear that Newton for the well-established systems of conservative forces (in the absence of absorption or emission of the particles of light having mass) predicted that the time is absolute in the Cartesian system of three dimensions, while in my discovery of dipolic photons (1993) I showed that in the correct explanation of the photoelectric effect the absorption of the dipolic photon contributes not only to the increase of the electron energy ΔΕ but also to the increase of the electron mass ΔΜ under a quantum length contraction and a quantum time dilation, which cannot be relater with Einstein’s ideas of space and time. (DISCOVERY OF LENGTH CONTRACTION). It is of interest to note that the great British philosopher and mathematician, Russell, in the conclusions of his second volume, "A History of Western Philosophy" (1945) wrote that the new philosophy developed in quantum physics would have to move away from Einstein's space-time. (HAWKING EINSTEIN RUSSELL). Category:Fundamental physics concepts